Doob–Meyer decomposition theorem

The Doob–Meyer decomposition theorem is a mathematical theorem that tells us how to split any random process (a way of predicting what will happen in the future based on information from the past) into two independent parts. The first part is a predictable part, called the "drift," which tells us how the process is changing normally over time. The second part is an unpredictable part, called the "martingale," which is randomly changing. Together, these two parts help us predict how the process will behave in the future.